Harmonic absorber

ABSTRACT

This is a harmonic absorber ( 14 ) for eliminating the harmonics occurring due to unbalanced loads in a network transformer ( 1 ), a power factor correction system ( 6 ) to correct the cos φ value of the system to which it has been connected and an electrical system comprising electrical loads ( 7 ), and it contains at least one harmonic hole circuit ( 13 ), which consists of power reactance inductors ( 13.1 ) and power capacitors ( 13.2 ), and a harmonic separating circuit ( 12 ), which separates the harmonics existing in the network from the other components in the network and then, in order to achieve the elimination of each individual harmonic achieved in this manner, applies them to the mentioned hole circuit ( 13 ).

FIELD OF THE INVENTION

This invention is based on a system which eliminates the harmonicvoltage and eliminates the harmonic currents which occur in low voltagenetworks.

BACKGROUND OF THE INVENTION

Harmonics are the periodic distortions caused on the sinusoidal wavesrelated to current, voltage or power. It is accepted that theiramplitudes are a combination of waveform, different frequencies and thevarious sinusoidal waves. Harmonics are mainly the results of thenon-linear loads of adjustable motor speed drivers or direct currentpower supplies of computers and televisions. These harmonics causeoverheating of transformers, conductors and motors.

When investigating the existing harmonic filters or absorbers, they wereinsufficient for eliminating these harmonics totally from the network.These products, which are mainly based on dynamic and passive harmonicfilters, are widely distributed in the market. The passive ones aredesigned to eliminate only a certain level of the harmonics. So they areincapable of eliminating the different levels of harmonics added to thenetworks or the different levels of harmonics on the currents thatdifferent loads create. In these systems, the existing passive harmonicfilter or absorber should be eliminated and the new harmonic levelshould be measured and a new passive harmonic filter or absorber shouldbe designed for the system. Additionally there will be a need to replacethe new compensation systems or change the power capacitors, because thenew total voltage generated after the new harmonics will be less thanthe amount of voltage of the compensation system's power capacitors. Theaim of the dynamic absorbers or the filters in the market today is toeasily make the adaptation of the additional loads or to remove theloads from the system. But in reality, after the measurements done, thissystem may only help to eliminate 1% or 2% of the other levels of theharmonics; this means there is no great effect and benefit. In fact ithas been observed that, while eliminating a certain percentage of theother levels of the harmonics, it triggered some levels of the harmonicsto higher values.

In international standards, institutions have legal restrictions toeliminate the harmonics or to lower the harmonics to certain levels.According to IEC (International Electric Cooperation) the total harmonicdistortion based on the voltage should not be more than 3%, and on thecurrent should not be more than 6%. Also based on the IEEE standard 519,all electrical systems should have lower harmonic distortions to protectagainst damage.

As a result, to eliminate the harmonics on the networks withouttriggering other levels of the harmonics and without adding anyadditional cost when there is a new load on the network which createsanother level of harmonics, these problems inspired us to work in thearea and make this invention.

SUMMARY OF THE INVENTION

The current invention is related to a harmonic absorber, which meets theabove-mentioned requirements, eliminates all of the disadvantages andbrings certain advantages.

The purpose of the invention is to put forward a structure that ensuresthe complete annihilation of all of the harmonics occurring in thenetwork.

Another purpose of the invention is to establish a harmonic absorbingstructure, which provides flexibility in the system, and without theneed for a structural change, takes an additional new harmonic absorberinto service, in case the equipment connections, which result in a riseof the harmonic currents, increase in the voltage network.

A further purpose of the invention is establishing a harmonic absorber,which does not necessitate any modification in the existing power factorcorrection structure in the system.

Another purpose of the invention is putting forward a harmonic absorberthat eliminates all harmonic currents and voltages and reduces theelectrical energy drawn from the network and hence, provides a decreasein the costs.

A further purpose for the invention is creating a harmonic absorber,which, apart from ensuring the reduction of energy losses in thefacility where it has been connected, causes the protection of the lifetimes of the equipment that may be damaged from the harmonics.

Furthermore, the invention is aimed at providing a harmonic absorberthat eliminates the power outages caused by harmonic currents andvoltages.

The invention provides a harmonic absorber according to claim 1 and amethod for absorbing harmonics according to claim 9. Optional featuresof the invention are set out in the dependent claims.

The structural and characteristic properties and the advantages of theinvention will be understood better after seeing the figures given belowand reading the detailed explanations written referring to these figuresand therefore the evaluation should be done considering these figuresand the detailed explanation.

BRIEF DESCRIPTION OF THE DRAWINGS

In FIG. 1, the open electrical circuit layout that shows the preferredstructure of the connection between the newly discovered harmonicabsorber and the system is given.

In FIG. 2, the detail of the open electrical circuit diagram related tothe structure that constitutes the newly discovered harmonic absorber isgiven.

THE REFERENCE NUMBERS USED FOR THE DRAWINGS

 1. Network transformer  2. Main switch  3. Current tranformer forcontrolling relays  4. Current transformer for measurement devices  4.1.Measurement devices and NH circuit-breaker  5. Power factor correctionprotection switch  6. Power factor correction circuit  6.1. A reactivecorrection power control relay  6.2. Circuit-breaker  6.3. The elementfor taking the power capacitor into service (contactor and/or tristor) 6.4. Power capacitor of Power factor correction  7. The loads connectedto the system  7.1. Switches for loads  8. Harmonic absorber specialconnection point  9. Harmonic absorber protection switch 10. Harmonicblock selection element 11. The element for taking the harmonic absorberblock into (contactor and/or tristor) 12. Harmonic separator 12.1. 5thharmonic transferors 12.2. 5th harmonic barrier circuit 12.2.1. Powerreactance inductor 12.2.2. Power capacitor 12.3. 9 th harmonic barriercircuit 12.4. 11 th harmonic barrier circuit 12.5. 7 th harmonictransferors 12.6. 5 th harmonic barrier circuit 12.7. 7 th harmonicbarrier circuit 12.8. 11 th harmonic barrier circuit 12.9. 9 th harmonictransferors 12.10. 5 th harmonic barrier circuit 12.11. 7 th harmonicbarrier circuit 12.12. 9 th harmonic barrier circuit 12.13. 11 thharmonic transferors 13. Harmonic hole 13.1. Harmonic hole powerreactance inductor 13.2. Harmonic hole power capacitors 14. Harmonicabsorber 15. Harmonic absorber circuit-breaker

DETAILED EXPLANATION OF THE INVENTION

In this detailed explanation, the preferred structuring of the harmonicabsorber (eliminator) is explained in an easily understood manner sothat it can be better understood, without any limiting influence.

There is a protection switch (9) selected according to the total valueof the harmonic currents, in the circuit acting as a protection element,which opens the circuit without damaging the circuit, and consequentlythe elements that may occur due to the increasing harmonics in thecircuit. Moreover, for the safety of the whole system, a main switch (2)should be included as a protection element. The connection point (8) ofthis element (2) is very important for the subject of the invention, theharmonic absorber (14), and is right after the current transformers (3,4) and the connection points of the other relays (6.1, 10), i.e. thedistribution point of the current drawn from the network. In otherwords, one end of the switch (2) should definitely be connected to thenetwork transformer and the other end, with the connection point (8) ofthe protective elements (5, 7.1, 9). Moreover, at the inputs of theharmonic absorber layers (14), load separators (11) with circuitbreakers are positioned. When choosing these load separators, it ispreferred to take into consideration a current (1/k)*1.2 times the totalharmonic current value. If a contactor is used as the NH circuitbreaker, to have the ideal working condition, it should be selected as azero conducting solid-state type or the super flinck (?) type.

The harmonic block selection unit (10), shown in FIG. 1, is preferably aharmonic relay available in the market and can be specially manufacturedby calculation according to the amount of the harmonic currents. Thepurpose of this relay (10) is to take the harmonic absorber (14) intoservice and to electrically open or close its elements. As theabove-mentioned element for taking into operation (11), contactors orzero conducting solid-state relays (contactors and/or thyristors) can beused. The current transformers (3, 4), which will be connected to thesystem, are selected according to the power of the transformer fromwhich they are fed and are responsible for measuring the currents drawnby the receivers (4.1, 6.1, 10) after them.

In order to take the power factor correction (6) into the circuit, areactive correction power control relay (6.1) can be used. Through thisrelay (6.1), it will be possible to select the line or lines where thepower capacitor (6.4), whose power factor correction will be realized,shall be taken into the circuit. In order to carry out this process, theelements whose above-mentioned control relay (6.1) outputs arepositioned in each line and preferably, which comprise contactors orthyristors are used for taking the power capacitor into service (6.3).By installing circuit-breakers at the beginning of each line, theprotection of the system is targeted.

The loads connected to the system (7) may be connected via relevantswitches (7.1) to the network. Thus, we arrive at a principal electricalcircuit (FIG. 1), which is used for connecting the loads (7), which arefed by the network transformer (1) and the power factor correction (6),which is used for power factor correction of the system, in an existingsystem. The mentioned structure is standard and represents theconnections, which are generally used in all establishments. Here theobjective is to focus on the important points for the connection of theharmonic absorber (14), which is the subject of the invention, to thesystem and to provide a better insight of how it works together with thesystem.

In order for the harmonic absorber (14) to be used effectively, asmentioned above, it should be connected to the system, especiallydirectly after the main switch (2). And directly after this connectionpoint, the current transformer (3), which will take the harmonicabsorber (14) appropriate for the system into service and which willfeed the harmonic block selection element (10), preferably a relay withmultiple outputs (10), is connected to the relevant line. This harmonicabsorber relay (10) takes into operation the harmonic absorber block orblocks (14), according to the types and amounts of the harmonic currentsoccurring in the network. A harmonic absorber block (14) comprises aharmonic barrier circuit (stopper) (12.2, 12.3, 12.4 etc.), whose valuesare calculated according to the types and amplitudes of the harmonicsdesired to be eliminated, as well as a harmonic separator withtransferors (12.1, 12.5 etc.). Here, the purpose is to apply theharmonic signals (waves) to the input of the harmonic hole circuit(regarded as a harmonic hole), after separating them from each other andthen, eliminate them here.

The harmonic hole (13) eliminates each of these harmonic currents thatcome from the harmonic separator (12) and that are separated from thenetwork and hence, ensures that these harmonic currents andconsequently, the harmonic voltages, which are, as mentioned in thebeginning, are created by non-linear loads and are unwanted because oftheir unwanted effects, are eliminated from the network and the networkis cleaned. In the system in FIG. 1, which has been designed for athree-phase system, preferably, a delta connected harmonic hole (13) isused. However, in three-phase and/or single-phase electric circuits, itis possible to realize the same function by making a star connection. Inthe harmonic hole (13); parallel connected harmonic hole power reactanceinductors (13.1) and power capacitors (13.2) are used. The dimensions ofthese are calculated according to the amplitude of the current drawnfrom the circuit and the components of the harmonic currents that arerequested to be eliminated, i.e. especially their frequencies. When theharmonic hole is used, in a three-phased system, as a delta circuit, asindicated in the preferred structure of FIG. 2, each corner of thetriangle is connected to the output of the harmonic separators takenfrom different phases. Moreover, instead of this structure, the harmonichole circuit can also be realized by applying each specific harmoniccurrent that is requested to be damped, separately to the circuitscomprising power reactance inductors and power capacitors, connected inparallel, as in the harmonic barrier circuits (12.2, 12.3 etc). However,as a technical expert can easily understand, the use of theabove-mentioned delta structure as a harmonic hole (13) reduces thenumber of connections and simplifies the system and hence, enables theestablishment of a meaningful structure.

The purpose of using the harmonic separator circuit (12) is to attractcertain components of harmonic currents to it, then separate them fromeach other and eliminate them by applying them to the harmonic hole(13). Access of harmonic currents, which are not desired to pass, to theharmonic hole (13) is prevented using harmonic barrier circuits (12.2,12.3, etc.), whose value is determined by calculating according to eachharmonic current. Attraction of each harmonic current to the harmonicseparator block (12) and then to the harmonic hole (13) is enabled byharmonic transferors (12.1, 12.5, and 12.9), which are designedaccording to the properties of harmonic current that is required topass. Here, the number of the harmonic barrier circuits used (12.2,12.3, etc), is proportional to the number of the harmonic currents thatare required to be damped. On the other hand, the number of harmonicabsorber blocks (14) may be any desired according to the amplitudes ofthe harmonic currents, which are required to be filtered from thenetwork. The harmonic currents are distributed to the mentioned harmonicblocks (12), via the above mentioned harmonic relay (10). Each output ofthis harmonic relay (10) triggers the load separating element (11) ofthe relevant harmonic block and thus connection or disconnection of therequired harmonic block (12) according to the specified conditions isprovided. The output of the harmonic relay (10) preferably works withmultiplexing logic. For example, when the amount of total harmoniccurrent exceeds the load capacity of a harmonic block (12), which isdesigned in accordance with a harmonic current of specific amplitude, itcan connect other blocks (12) in accordance with the requirements. So,the total harmonic current is distributed to the separator blocks (12).

In the invention, when examined as a practical method, to attenuate andto absorb the harmonic currents, it seems necessary to separate them,primarily from the network and then from each other. Here, via aharmonic separator (12), which enters into the circuit at theappropriate time according to the values of the harmonic currents, theharmonic currents are separated from the network and from each other.Through power reactance inductors wound at values suitable for eachharmonic current component, these harmonic currents are drawn towardsthe above-mentioned harmonic separator (12). Moreover, they areeliminated by a harmonic hole (13), established for the damping of theindividual harmonic currents, achieved at the output of the harmonicseparator (12). The harmonic hole here (13), as mentioned above, can bemade of star or delta connected parallel power reactance inductors(13.1) and power capacitors (13.2) orit can be made of parallelconnected power reactance inductors and power capacitors, designedindividually for each harmonic current and positioned dispersedly. Inimplementation, the most preferred way is the triad connection, as shownin FIG. 1 and FIG. 2.

For example, in the structure preferred in FIG. 2, the harmonicseparator draws the 5th, 7th, 9th and 11th harmonics from the networkand after separating them, conveys them to the harmonic hole (13). The5th harmonic transferor (12.1) draws only this harmonic current toitself and does not affect the other harmonic currents. The 5th, 9th and11th harmonic barrier circuits (12.6, 12.7 and 12.8), belonging to thesecond branch, are serially connected and these harmonic currents arefiltered and only the 7th harmonic is conveyed to the harmonic hole (13)via a power reactance inductor (12.5). Similarly, in the third branch,the 5th, 7th and 11th harmonic current barrier circuits (12.6, 12.7, and12.8) prevent the passage of these harmonics and via a 9th harmonictransferor (12.9), serially connected to these, the 9th harmonic isconveyed to the output. And in order to pass the 11th harmonic, the 5th,7th and 9th harmonic barrier circuits (12.10, 12.11 and 12.13) and an11th harmonic transferor is used. As mentioned before, the number ofbranches where each individual harmonic current shall be drawn and thenumber of harmonic barrier circuits (12.2, 12.3, etc.) can varyaccording to the number of harmonic currents that are requested to beeliminated.

In determining the real values of a harmonic absorber that can be usedin such a system an approach may be provided as follows, by calculatingthe numeric values with formulae and without forming a limiting factor:

First, a measurement is done with a harmonic analyzer at the Low Voltagenetwork.

-   -   1) S, transformer power in VA.    -   2) UK, is obtained from the transformer's label.    -   3) Harmonic currents are measured.    -   I₃=3^(rd) harmonic current value in Amperes (A).    -   I₅=5^(th) harmonic current value in Amperes (A).    -   I₇=7^(th) harmonic current value in Amperes (A).    -   I₉=9^(th) harmonic current value in Amperes (A).    -   I₁₁=11^(th) harmonic current value in Amperes (A).

The 3^(rd) harmonic current value disappears in the network because ofdelta connected motors or heaters present in the low voltage network.Therefore a unit to eliminate this value is not placed in the harmonicabsorber. However, if there are too few or no delta connected takers inthe low voltage system, the third harmonic unit is added to the system.

In our sample diagram, practically the most common5^(th)-7^(th)-9^(th)-11^(th) harmonic values are considered and drawn.If other harmonic levels are encountered during measurements,principally the numbers of the harmonic collector circuits we implementare increased. In accordance with the requirements in the system, one ormore of the 5^(th)-7^(th)-9^(th)-11^(th) harmonic collectors may beremoved.

The example below may be presented in order to show the measurements innumeric values:

S = 1600 kVA u_(k) = %6 u = 400 V I = 2000 A I₅ = %20 I = 400 A V₅ =8.88 V I₇ = %25 I = 500 A V₇ = 15.55 V I₉ = %15 I = 300 A V₉ = 11.99 VI₁₁ = %10 I = 200 A V₅ = 9.77 V

Total harmonic current I₂=√{square root over (I₅ ²+I₇ ²+I₉ ²+I₁₁ ²)}√{square root over (400²+500²+300²+200²)}=734,84A The calculation of thevalue of the power capacitor to eliminate these harmonic currents:

Q=√{square root over (3)}*I _(d) *u=√{square root over(3)}*734,84*400=509112 VAr≈500 kVAr

Because the most economical solution for the application is 50 kVAr; itis calculated as

$k = {\frac{500}{50} = 10}$${C_{\Delta} = {\frac{Q_{c}}{3*u^{2}*100\pi} = {\frac{500}{3*400^{2}*100\pi} = 331}}},{4393\mspace{14mu} {µF}}$C_(λ) = 3 * C_(Δ) = 3 * 331, 4393 = 994, 31779  µF

After these calculations, to find the value of the LA power reactanceinductor:

${L_{\Delta} = {\frac{1}{C_{\Delta}*100\pi} = {\frac{10^{6}}{331,{4393*100\pi}} = 30.545}}},{46\mspace{14mu} {µH}}$

We accept L_(Δ)=30.550 μH, because of the manufacturing possibilitiesfor power reactance inductor (due to which we should round the lastdigits to the value of 10 or 10 times).

${L_{\lambda} = {\frac{L_{\Delta}}{3} = {\frac{30.550}{3} = 10.183}}},{33\mspace{14mu} {µH}}$

When the harmonic currents are passed to the collector circuits:

${x_{5} = {\frac{V_{5}}{I_{5}^{\prime}} = {\frac{8,88}{\left( {400\text{/}10} \right)} = 0}}},{222\mspace{14mu} \Omega}$x_(A 5) = L₅ * 500π

The 5th harmonic current, may only pass -A- section and than go to -O-harmonic hole, because there are 5th harmonic barriers in the othercircuits.

$\begin{matrix}{\frac{1}{x_{C\; 5}} = {\frac{1}{L_{1\lambda}*500\pi} - {C_{\lambda}*500\; \pi}}} \\{{= {\frac{10^{6}}{10.183,{33*500\pi}} - 994}},{3179*10^{- 6}*500\pi}}\end{matrix}$      x_(C 5) = −0, 6666627     x₅ = 0, 222 = L₅ * 500π − 0, 66666627     L₅ = 565, 512627 ≈ 570  µH(rounding  of)$\mspace{79mu} {I_{7}^{\prime} = {\frac{500}{10} = {50\mspace{14mu} A}}}$

Here we calculate the value of the power capacitors in this circuit,because the part of this harmonic current with the higher value willpass from B-E circuit:

C_(5.1)=C_(9.1)=C_(11.1)

Q ₇=√{square root over (3)}*50*400=34.640 Var

We round off this value to Q₇=40 kVAr.

${C_{5.1} = {C_{9.1} = {C_{11.1} = {\frac{40.000}{3*400^{2}*100\pi} = 265}}}},{15\mspace{14mu} {µF}}$

The calculation of the values of the power reactance inductors will beas below, because these power capacitors will be used as the 5-9-11 thharmonic barrier circuits.

$\begin{matrix}{L_{5.1} = \frac{1}{C_{5.1}*\left( {500\; \pi} \right)^{2}}} \\{= \frac{10^{6}}{265,{15*\left( {500\pi} \right)^{2}}}} \\{{= 1.527},{28 \approx {1.530\mspace{14mu} {µH}}}}\end{matrix}$ $\begin{matrix}{L_{9.1} = \frac{1}{C_{9.1}*\left( {900\pi} \right)^{2}}} \\{= \frac{10^{6}}{265,{15*\left( {900\pi} \right)^{2}}}} \\{{= 471},{38 \approx {470\mspace{20mu} {µH}}}}\end{matrix}$ $\begin{matrix}{L_{11.1} = \frac{1}{C_{11.1}*\left( {1100\pi} \right)^{2}}} \\{= \frac{10^{6}}{265,{15*\left( {1100\pi} \right)^{2}}}} \\{{= 315},{55 \approx {320\mspace{14mu} {µH}}}}\end{matrix}$ $\begin{matrix}{x_{A\; 7} = {L_{5}*700\pi}} \\{= {570*10^{{- 6}\;}*700\pi}} \\{{= 1},{254\mspace{11mu} \Omega}}\end{matrix}$ $\begin{matrix}{\frac{1}{x_{B\; 7}} = {\frac{1}{L_{5.1}*700\pi} - {C_{5.1}*700\pi}}} \\{{= {\frac{10^{6}}{1.530\;*700\pi} - 265}},{15*10^{- 6}*700\pi}}\end{matrix}$ x_(B 7) = −3, 4935539  Ω $\begin{matrix}{\frac{1}{x_{C\; 7}} = {\frac{1}{L_{9.1}*700\pi} - {C_{9.1}*700\pi}}} \\{{= {\frac{10^{6}}{470*700\pi} - 265}},{15*10^{- 6}*700\pi}}\end{matrix}$ x_(C 7) = 2, 605605  Ω

$\begin{matrix}{\frac{1}{x_{D\; 7}} = {\frac{1}{L_{11.1}*700\pi} - {C_{11.1}*700\pi}}} \\{{= {\frac{10^{6\;}}{320*700\pi} - 265}},{15*10^{- 6}*700\pi}}\end{matrix}$ x_(D 7) = 1, 194565  Ωx_(E 7) = L₇ * 700π = 2.200 * L₇x_((B − E)7) = −3, 4935539 + 2, 605605 + 1, 194565 + 2.200L₇${x_{({B - E})} = {{2.200L_{7}} + 0}},{{306616\begin{matrix}{\frac{1}{x_{{({A - E})}\; 7}} = {\frac{1}{1,254} + \frac{1}{{2.200L_{7}} + {0,306616}}}} \\{= \frac{{{2.200L_{7}} + 1},560616}{2.758,{{8L_{7}} + {0,384496}}}}\end{matrix}x_{{({A - E})}7}} = {{\frac{2.758,{{8L_{7}} + {0,384496}}}{{2.200L_{7}} + {1,560616}}\begin{matrix}{\frac{1}{x_{O\; 7}} = {\frac{1}{L_{\lambda}*700\pi} - {C_{\lambda}*700\pi}}} \\{{= {\frac{10^{6}}{10.183,{33*700\pi}} - 994}},{3179*10^{- 6}*700\pi}}\end{matrix}x_{O\; 7}} = {- 0}}},{466665\mspace{20mu} \Omega}$

$x_{7} = {\frac{V_{7}}{I_{7}} = {x_{{({E - A})}7} + x_{O\; 7}}}$$\begin{matrix}{x_{7} = \frac{15,55}{\left( {500/10} \right)}} \\{= {0,311}} \\{= {\frac{2.758,{{8L_{7}} + 0},384496}{{{2.200L_{7}} + 1},560616} - {0,466665}}}\end{matrix}$$0,{777665 = \frac{2.758,{{8L_{7}} + 0},384496}{{{2.200L_{7}} + 1},560616}}$1.710, 863L₇ + 1, 213636 = 2.758, 8L₇ + 0, 3844961.047, 937L₇ = 0, 82914L₇ = 791, 21 ≈ 790  µH$I_{9}^{\prime} = {\frac{300}{10} = {30\mspace{20mu} A}}$

Here, we calculate the power capacitor values in this circuit, becausethe higher value of this harmonic current will pass from A and (F-I)circuits: C_(5.2)=C_(7.1)=C_(9.2)

Q ₉=√{square root over (3)}*30*400=20.784 Var

We round off this value as Q₇=30 kVAr.

${C_{5.2} = {C_{7.1} = {C_{9.2} = {\frac{30.000}{3*400^{2}*100\pi} = 198}}}},{8636\mspace{14mu} {µF}}$

The calculation of the values of the power reactance inductors will beas below, because these power capacitors will be used as the 5-7-11 thharmonic barrier circuits.

$\begin{matrix}{L_{5.2} = \frac{1}{C_{5.2}*\left( {500\pi} \right)^{2}}} \\{= \frac{10^{6}}{198,{8636*\left( {500\pi} \right)^{2}}}} \\{{= 2.036},{36 \approx {2.040\mspace{14mu} {µH}}}}\end{matrix}$ $\begin{matrix}{L_{7.1} = \frac{1}{C_{7.1}*\left( {700\pi} \right)^{2}}} \\{= \frac{10^{6}}{198,{8636*\left( {700\pi} \right)^{2}}}} \\{{= 1.038},{96 \approx {1.040\mspace{14mu} {µH}}}}\end{matrix}$ $\begin{matrix}{L_{11.2} = \frac{1}{C_{11.2}*\left( {1100\pi} \right)^{2}}} \\{= \frac{10^{6}}{198,{8636 - \left( {1100\pi} \right)^{2}}}} \\{{= 420},{736 \approx {420\mspace{14mu} {µH}}}}\end{matrix}$x_(A 9) = L₅ * 900π = 570 * 10⁻⁶ * 900π = 1, 6122857  Ω$\begin{matrix}{\frac{1}{x_{F\; 9}} = {\frac{1}{L_{5.2}*900\pi} - {C_{5.2}*900\pi}}} \\{{= {\frac{10^{6}}{2.040*900\pi} - 198}},{8636*10^{- 6}*900\pi}}\end{matrix}$ x_(F 9) = −2, 5693846  Ω

$\begin{matrix}{\frac{1}{x_{G\; 9}} = {\frac{1}{L_{7.1}*900\pi} - {C_{7.1}*900\pi}}} \\{{= {\frac{10^{6}}{1.040*900\pi} - 198}},{8636*10^{- 6}*900\pi}}\end{matrix}$ x_(G 9) = −4, 4931288  Ω $\begin{matrix}{\frac{1}{x_{H\; 9}} = {\frac{1}{L_{11.2}*900\pi} - {C_{11.2}*900\pi}}} \\{{= {\frac{10^{6}}{420*900\pi} - 198}},{8636*10^{- 6}*900\pi}}\end{matrix}$ x_(H 9) = 3, 58100847  Ω x_(I 9) = L₉ * 900πx_((F − I)9) = −2, 5693846 − 4, 4931288 + 3, 58100847 + (L₉ * 900π)x_((F − I)9) = (L₉ * 900π) − 3, 4815049

$\begin{matrix}{\frac{1}{x_{{({A - I})}9}} = {\frac{1}{x_{A\; 9}} + \frac{1}{x_{{({F - I})}9}}}} \\{= {\frac{1}{1,6122857} + \frac{1}{{\left( {L_{9}*900\pi} \right) - 3},4815049}}} \\{= \frac{{\left( {L_{9}*900\pi} \right) - 1},8692192}{4.560,{{4652657L_{9}} - 5},61318}}\end{matrix}$$x_{{({A - I})}9} = \frac{4.560,{{4652657L_{9}} - 5},61318}{{\left( {L_{9}*900\pi} \right) - 1},8692192}$$\begin{matrix}{\frac{1}{x_{O\; 9}} = {\frac{1}{L_{\lambda}*900\pi} - {C_{\lambda}*900\pi}}} \\{{= {\frac{10^{6}}{10.183,{33*900\pi}} - 994}},{3179*10^{- 6}*900\pi}}\end{matrix}$ x_(O 9) = −0, 359994  Ω

$x_{9} = \frac{V_{9}}{I_{7}^{\prime}}$ $\begin{matrix}{x_{9} = \frac{11,99}{\left( {300/10} \right)}} \\{{= 0},39966} \\{{= {\frac{4.560,{{4652657L_{9}} - 5},61318}{{\left( {L_{9}*900\pi} \right) - 1},86921092} - 0}},3599994}\end{matrix}$$0,{7596654 = \frac{4.560,{{4652657L_{9}} - 5},61318}{{\left( {L_{9}*900\pi} \right) - 1},86921092}}$2.148, 7678457L₉ − 1, 419981 = 4.560, 4652657L₉ − 5, 613182.411, 69742L₉ = 4, 193199 L₉ − 1.738, 69 ≈ 1.740  μH$I_{11}^{\prime} = {\frac{200}{10} = {20\mspace{14mu} A}}$

Here, we calculate the power capacitor values in this circuit, becausethe higher value of this harmonic current will pass from A and (K-N)circuits

Q ₁₁=√{square root over (3)}*20*400=13.856,4 VAr

We round off this value to Q₁₁=20 kVAr.

${C_{5.2} = {C_{7.1} = {C_{9.2} = {\frac{20.000}{3*400^{2}*100\pi} = 132}}}},{57\mspace{14mu} {µF}}$

The calculation of the values of the power reactance inductors will beas below, because these power capacitors will be used as the 5-7-9thharmonic barrier circuits.

$\begin{matrix}{L_{5.3} = \frac{1}{C_{5.3}*\left( {500\pi} \right)^{2}}} \\{= \frac{10^{6}}{132,{57*\left( {500\pi} \right)^{2}}}} \\{{= 3.054},{67 \approx {3.060\mspace{20mu} {µH}}}}\end{matrix}$ $\begin{matrix}{L_{7.2} = \frac{1}{C_{7.2}*\left( {700\pi} \right)^{2}}} \\{= \frac{10^{6}}{132,{57*\left( {700\pi} \right)^{2}}}} \\{{= 1.558},{5 \approx {1.560\mspace{14mu} {µH}}}}\end{matrix}$ $\begin{matrix}{L_{9.2} = \frac{1}{C_{9.2}*\left( {900\pi} \right)^{2}}} \\{= \frac{10^{6}}{132,{57*\left( {900\pi} \right)^{2}}}} \\{{= 942},{8 \approx {940\mspace{11mu} {µH}}}}\end{matrix}$x_(A 11) = L₅ * 1100π = 570 * 10⁻⁶ * 1100π = 1, 970571  Ω$\begin{matrix}{\frac{1}{x_{K\; 11}} = {\frac{1}{L_{5.3}*1.100\pi} - {C_{5.3}*1.100\pi}}} \\{{= {\frac{10^{6}}{3.060*1.100\pi} - 132}},{57*10^{- 6}*1.100\pi}}\end{matrix}$ x_(K 11) = −2, 748874  Ω

$\begin{matrix}{\frac{1}{x_{L\; 11}} = {\frac{1}{L_{7.2}*1.100\pi} - {C_{7.2}*1.100\pi}}} \\{{= {\frac{10^{6}}{1.560*1.100\pi} - 132}},{57*10^{- 6}*1.100\pi}}\end{matrix}$ x_(L 119) = −3, 6644427  Ω $\begin{matrix}{\frac{1}{x_{M\; 11}} = {\frac{1}{L_{9.2}*1.100\pi} - {C_{9.2}*1.100\pi}}} \\{{= {\frac{10^{6}}{940*1.100\pi} - 132}},{57*10^{- 6}*1.100\pi}}\end{matrix}$ x_(M 11) = −6, 6403677  Ω x_(N 11) = L₁₁ * 1.100π x_((K − N)11) = −2, 748874 − 3, 6644427 − 6, 6403677 + (L₁₁ * 1.100π)x_((K − N)11) = (L₁₁ * 1.100π) − 13, 0536844

$\begin{matrix}{\frac{1}{x_{{({A - N})}11}} = {\frac{1}{1,970571} + \frac{1}{{\left( {L_{11}*1.100\pi} \right) - 13},0536844}}} \\{= \frac{{\left( {L_{11}*1.100\pi} \right) - 11},0831134}{6.812,{{545457L_{11}} - 25},7232119}}\end{matrix}$$x_{{({A - N})}11} = \frac{6.812,{{545457L_{11}} - 25},7232119}{{\left( {L_{11}*1.100\pi} \right) - 11},08311134}$$\begin{matrix}{\frac{1}{x_{O\; 11}} = {\frac{1}{L_{\lambda}*1.100\pi} - {C_{\lambda}*1.100\pi}}} \\{{= {\frac{10^{6}}{10.183,{33*1.100\pi}} - 994}},{3179*10^{- 6}*1.100\pi}}\end{matrix}$ x_(O 11) = −0, 293333  Ω$x_{11} = \frac{V_{11}}{I_{11}^{\prime}}$ $\begin{matrix}{x_{11} = \frac{9,77}{\left( {200/10} \right)}} \\{{= 0},4885} \\{{= {\frac{6.812,{{545457L_{11}} - 25},7232119}{{\left( {L_{11}*1.100\pi} \right) - 11},0831134} - 0}},293333}\end{matrix}$$0,{781833 = \frac{6.812,{{545457L_{11}} - 25},7232119}{{\left( {L_{11}*1.100\pi} \right) - 11},0831134}}$2.702, 908371L₁₁ − 8, 665143 = 6.812, 545457L₁₁ − 25, 72321194.109, 637086L₁₁ = 17, 0580689 L₁₁ = 4.150, 748 ≈ 4.150  µH

It is possible to use a solid-state relay, which has an instant replycapacity with zero transition, in the example of the harmonic absorberdescribed above, instead of a contactor with slow reply capacity.

If the example we have given above, is investigated in detail, it willbe easily understood that the current and the voltage values on theharmonic levels of the power reactance inductors are calculated asfollows:

I-50  Hz x_(A 1) = L₅ * 10⁻⁶ * 100 π = 570 * 10⁻⁶ * 100 π = 0, 1791428${\frac{1}{x_{B\; 1}} = {\frac{10^{6}}{1530*100\; \pi} - 265}},{{15*10^{- 6}*100\; {\pi x_{B\; 1}}} = 0},{{50093\frac{1}{x_{C\; 1}}} = {\frac{1}{L_{9.1}*100\; \pi} - {C_{9.1}*100\; \pi {\frac{1}{x_{C\; 1}} = {\frac{10^{6}}{L_{9.1}*100\; \pi} - 265}}}}},{{15*10^{- 6}*100\; {\pi x_{C\; 1}}} = 0},{{149555\frac{1}{x_{D\; 1}}} = {\frac{1}{L_{11.1}*100\; \pi} - {C_{11.1}*100\; \pi {\frac{1}{x_{D\; 1}} = {\frac{10^{6}}{320*100\; \pi} - 265}}}}},{{15*10^{- 6}*100\; {\pi x_{D\; 1}}} = 0},{101421{x_{E\; 1} = {{L_{7}*100\; \pi} = {{790*10^{- 6}*100\; \pi} = 0}}}},{{248285x_{{({B - E})}1}} = 1},000191$

$\frac{1}{x_{F\; 1}} = {\frac{1}{L_{5.2}*100\; \pi} - {C_{5.2}*100\; \pi}}$$\begin{matrix}{{\frac{1}{x_{F\; 1}} = {\frac{10^{6}}{2040*100\; \pi} - 198}},{8636*10^{- 6}*100\; {\pi x_{F\; 1}}}} \\{{= 0},6679068}\end{matrix}$$\frac{1}{x_{G\; 1}} = {\frac{1}{L_{7.1}*100\; \pi} - {C_{7.1}*100\; \pi}}$$\begin{matrix}{{\frac{1}{x_{G\; 1}} = {\frac{10^{6}}{1040*100\; \pi} - 198}},{8636*10^{- 6}*100\; {\pi x_{G\; 1}}}} \\{{= 0},3836736}\end{matrix}$$\frac{1}{x_{H\; 1}} = {\frac{1}{L_{11.2}*100\; \pi} - {C_{11.2}*100\; \pi}}$$\begin{matrix}{{\frac{1}{x_{H\; 1}} = {\frac{10^{6}}{420*100\; \pi} - 198}},{8636*10^{- 6}*100\; {\pi x_{H\; 1}}}} \\{{= 0},133098}\end{matrix}$x_(I 1) = L₉ * 100 π = 1740 * 10⁻⁶ * 100 π = 0, 546857x_((F − I)1) = 1, 681535

$\frac{1}{x_{K\; 1}} = {\frac{1}{L_{5.3}*100\; \pi} - {C_{5.3}*100\; \pi}}$${\frac{1}{x_{K\; 1}} = {\frac{10^{6}}{3060*100\; \pi} - 132}},{{57*10^{- 6}*100\; {\pi x_{K\; 1}}} = 1},{{001858\frac{1}{x_{L\; 1}}} = {\frac{1}{L_{7.2}*100\; \pi} - {C_{7.2}*100\; \pi {\frac{1}{x_{L\; 1}} = {\frac{10^{6}}{1560*100\; \pi} - 132}}}}},{{57*10^{- 6}*100\; {\pi x_{L\; 1}}} = 0},{{5005099\frac{1}{x_{M\; 1}}} = {\frac{10^{6}}{L_{9.2}*100\; \pi} - {C_{9.2}*100\; \pi {\frac{1}{x_{M\; 1}} = {\frac{10^{6}}{940*100\; \pi} - 132}}}}},{{57*10^{- 6}*100\; {\pi x_{M\; 1}}} = 0},{2991103{x_{N\; 1} = {{L_{11}*00\; \pi} = {{4150*10^{- 6}*100\; \pi} = 1}}}},{3042857{x_{{({K - N})}\; 1} = 3}},{{1057639\frac{1}{x_{{({A - N})}1}}} = {\frac{1}{x_{A\; 1}} + \frac{1}{x_{{({B - E})}1}} + \frac{1}{x_{{({F - I})}1}} + \frac{1}{x_{{({K - N})}\; 1}}}}$

$\frac{1}{x_{{({A - N})}1}} = {\frac{1}{0,1791428} + \frac{1}{1,000191} + \frac{1}{1,681535} + \frac{1}{3,1057639}}$x_((A − N)1) = 0, 1333577$\frac{1}{x_{O\; 1}} = {\frac{1}{L_{\lambda}*100\; \pi} - {C_{\lambda}*100\; \pi}}$${\frac{1}{x_{O\; 1}} = {\frac{10^{6}}{10.183,{33*100\; \pi}} - 994}},{\left. {3179*10^{- 6}*100\; \pi}\rightarrow x_{O\; 1} \right. = {- 21.595}},8422095$$\begin{matrix}{x_{1} = {x_{{({A - N})}1} + x_{O\; 1}}} \\{{= 0},{1333577 - 21.595},8422095} \\{{= {- 21.595}},7088518}\end{matrix}$ $I_{1} = \frac{V_{1}}{x_{1}}$${V_{1} = {\frac{400}{\sqrt{3}} = 230}},9401076$${I_{1} = {\frac{230,9401076}{{- 21.595},7088518} = {- 0}}},{01069379\mspace{14mu} A}$$\begin{matrix}{V_{1} = {V_{A\; 1} + V_{O\; 1}}} \\{= {V_{B\; 1} + V_{C\; 1} + V_{D\; 1} + V_{E\; 1} + V_{O\; 1}}} \\{= {V_{F\; 1} + V_{G\; 1} + V_{H\; 1} + V_{I\; 1} + V_{O\; 1}}} \\{= {V_{K\; 1} + V_{L\; 1} + V_{M\; 1} + V_{N\; 1} + V_{O\; 1}}}\end{matrix}$

$\begin{matrix}{V_{O\; 1} = {I_{1}*x_{O\; 1}}} \\{{= {- 0}},{01069379*{- 21.595}},8422095} \\{{= 230},941401}\end{matrix}$ $\begin{matrix}{V_{A\; 1} = {V_{1} - V_{O\; 1}}} \\{{= 230},{9401076 - 230},941401} \\{{= {- 0}},0012934}\end{matrix}$ $\begin{matrix}{I_{A\; 1} = \frac{V_{A\; 1}}{x_{A\; 1}}} \\{= \frac{{- 0},0012934}{0,1791428}} \\{{= {- 0}},{0072199\mspace{14mu} A}}\end{matrix}$ (The  current  passing  on  L₅  at  50  Hz)$\begin{matrix}{I_{{({B - E})}1} = \frac{V_{A\; 1}}{x_{{({B - E})}1}}} \\{= \frac{{- 0},0012934}{1,000191}} \\{{= {- 0}},{001293\mspace{14mu} A}}\end{matrix}$ (The  current  passing  on  L₇  at  50  Hz)$\begin{matrix}{V_{B\; 1} = {I_{{({B - E})}1}*x_{B\; 1}}} \\{{= {- 0}},{01293*0},50093} \\{{= {- 0}},{0006477\mspace{14mu} V}}\end{matrix}$ $\begin{matrix}{I_{B\; 1.1} = \frac{V_{B\; 1}}{L_{5.1}*100\; \pi}} \\{= \frac{{- 0},{0006477*10^{6}}}{1560*100\; \pi}} \\{{= {- 0}},{001321\mspace{14mu} A}}\end{matrix}$(The  current  passing  on  L_(5.1)  at  50  Hz)$\begin{matrix}{I_{B\; 2.1} = {V_{B\; 1}*C_{5.1}*100\; \pi}} \\{{= {- 0}},{0006477*{- 265}},{15*10^{- 6}*100\; \pi}} \\{{= 0},{0000539\mspace{14mu} A}}\end{matrix}$(The  current  passing  on  C_(5.1)  at  50  Hz)

$\begin{matrix}{V_{C\; 1} = {I_{{({B - E})}1}*x_{C\; 1}}} \\{{= {- 0}},{001293*0},149555} \\{{= {- 0}},{000193\mspace{14mu} V}}\end{matrix}$ $\begin{matrix}{I_{C\; 1.1} = \frac{V_{C\; 1}}{L_{9.1}*100\; \pi}} \\{= \frac{{- 0},{000193*10^{6}}}{470*100\; \pi}} \\{{= {- 0}},{001309\mspace{14mu} A}}\end{matrix}$(The  current  passing  on  L_(9.1)  at  50  Hz)$\begin{matrix}{I_{C\; 2.1} = {V_{C\; 1}*C_{9.1}*100\; \pi}} \\{{= {- 0}},{0006477*{- 265}},{15*10^{- 6}*100\; \pi}} \\{{= 0},{000016\mspace{14mu} A}}\end{matrix}$(The  current  passing  on  C_(9.1)  at  50  Hz)$\begin{matrix}{V_{D\; 1} = {I_{{({B - E})}1}*x_{D\; 1}}} \\{{= {- 0}},{001293*0},101421} \\{{= {- 0}},{000131\mspace{14mu} V}}\end{matrix}$ $\begin{matrix}{I_{D\; 1.1} = \frac{V_{D\; 1}}{L_{11.1}*100\; \pi}} \\{= \frac{{- 0},{000131*10^{6}}}{320*100\; \pi}} \\{{= {- 0}},{0013\mspace{14mu} A}}\end{matrix}$(The  current  passing  on  L_(11.1)  at  50  Hz)$\begin{matrix}{I_{D\; 2.1} = {V_{D\; 1}*C_{11.1}*100\; \pi}} \\{{= {- 0}},{000131*{- 265}},{15*10^{- 6}*100\; \pi}} \\{{= 0},{0000109\mspace{14mu} A}}\end{matrix}$(The  current  passing  on  C_(11.1)  at  50  Hz)

$\begin{matrix}{V_{E\; 1} = {I_{({B - E})}*x_{E\; 1}}} \\{{= {- 0}},{001293*0},248285} \\{{= {- 0}},{000321\mspace{14mu} V}}\end{matrix}$ $\begin{matrix}{I_{{({F - I})}1} = \frac{V_{A\; 1}}{x_{{({F - I})}1}}} \\{= \frac{{- 0},0012934}{1,681535}} \\{{= {- 0}},{000769\mspace{14mu} A}}\end{matrix}$ (The  current  passing  on  L₉  at  50  Hz)$\begin{matrix}{V_{F\; 1} = {I_{{({F - I})}1}*x_{F\; 1}}} \\{{= {- 0}},{000769*0},6679068} \\{{= {- 0}},{0005136\mspace{14mu} V}}\end{matrix}$ $\begin{matrix}{I_{F\; 1.1} = \frac{V_{F\; 1}}{L_{5.2}*100\; \pi}} \\{= \frac{{- 0},{0005136*10^{6}}}{2040*100\; \pi}} \\{{= {- 0}},{000801\mspace{14mu} A}}\end{matrix}$(The  current  passing  on  L_(5.2)  at  50  Hz)$\begin{matrix}{I_{F\; 2.1} = {V_{F\; 1}*C_{5.2}*100\; \pi}} \\{{= {- 0}},{0005136*{- 198}},{8636*10^{- 6}*100\; \pi}} \\{{= 0},{00032\mspace{14mu} A}}\end{matrix}$(The  current  passing  on  C_(5.2)  at  50  Hz)$\begin{matrix}{V_{G\; 1} = {I_{{({F - I})}1}*x_{G\; 1}}} \\{{= {- 0}},{0005136*0},3336736} \\{{= {- 0}},{000171\mspace{14mu} V}}\end{matrix}$

$\begin{matrix}{I_{G\; 1.1} = \frac{V_{G\; 1}}{L_{7.1}*100\; \pi}} \\{= \frac{{- 0},{000171*10^{6}}}{1040*100\; \pi}} \\{{= {- 0}},{000523\mspace{14mu} A}}\end{matrix}$(The  current  passing  on  L_(7.1)  at  50  Hz)$\begin{matrix}{I_{G\; 2.1} = {V_{G\; 1}*C_{7.1}*100\; \pi}} \\{{= {- 0}},{000171*{- 198}},{8636*10^{- 6}*100\; \pi}} \\{{= 0},{00001\mspace{14mu} A}}\end{matrix}$(The  current  passing  on  C_(7.1)  at  50  Hz)$\begin{matrix}{V_{H\; 1} = {I_{{({F - I})}1}*x_{H\; 1}}} \\{{= {- 0}},{0005136*0},133098} \\{{= {- 0}},{000068\mspace{14mu} V}}\end{matrix}$ $\begin{matrix}{I_{H\; 1.1} = {\frac{V_{H\; 1}}{L_{11.2}*100\; \pi}\frac{{{- 0},{000068\;*10^{6}}}\mspace{11mu}}{420*100\; \pi}}} \\{{= {- 0}},{000515\mspace{14mu} A}}\end{matrix}$(The  current  passing  on  L_(11.2)  at  50  Hz)$\begin{matrix}{I_{H\; 2.1} = {V_{H\; 1}*C_{11.2}*100\; \pi}} \\{{= {- 0}},{000068*{- 198}},{8636*10^{- 6}*100\; \pi}} \\{{= 0},{000004\mspace{14mu} A}}\end{matrix}$(The  current  passing  on  C_(11.2)  at  50  Hz)$\begin{matrix}{V_{I{.1}} = {I_{{({F - I})}1}*x_{1}}} \\{{= {- 0}},{0005136*0},546857} \\{{= {- 0}},{00028\mspace{14mu} V}}\end{matrix}$

$\begin{matrix}{I_{{({K - N})}1} = \frac{V_{A\; 1}}{x_{{({K - N})}1}}} \\{= \frac{{- 0},00028}{{- 3},1057639}} \\{{= {- 0}},{00009\mspace{14mu} A}}\end{matrix}$ (The  current  passing  on  L₁₁  at  50  Hz)V_(K 1) = I_((K − N)1) * x_(K 1) = −0, 00009 * 1, 001858 = 0, 00009  V$\begin{matrix}{I_{K\; 1.1} = \frac{V_{K\; 1}}{L_{5.3}*100\; \pi}} \\{= \frac{{- 0},{00009*10^{6}}}{3060*100\; \pi}} \\{{= {- 0}},{000093\mspace{14mu} A}}\end{matrix}$(The  current  passing  on  L_(5.3)  at  50  Hz)$\begin{matrix}{I_{K\; 2.1} = {V_{K\; 1}*C_{5.3}*100\; \pi}} \\{{= {- 0}},{00009*{- 132}},{57*10^{- 6}*100\; \pi}} \\{{= 0},{0000037\mspace{14mu} A}}\end{matrix}$(The  current  passing  on  C_(5.3)  at  50  Hz)V_(L 1) = I_((K − N)1) * x_(L 1) = −0, 00009 * 0, 5005099 = −0, 000045  V$\begin{matrix}{I_{L\; 1.1} = \frac{V_{L\; 1}}{L_{7.2}*100\; \pi}} \\{= \frac{{- 0},{000045*10^{6}}}{1560*100\; \pi}} \\{{= {- 0}},{000091\mspace{14mu} A}}\end{matrix}$(The  current  passing  on  L_(7.2)  at  50  Hz)$\begin{matrix}{I_{L\; 2.1} = {V_{L\; 1}*C_{7.2}*100\; \pi}} \\{{= {- 0}},{000045*{- 132}},{57*10^{- 6}*100\; \pi}} \\{{= 0},{0000018\mspace{14mu} A}}\end{matrix}$(The  current  passing  on  C_(7.2)  at  50  Hz)

 V_(M 1) = I_((K − N)1) * x_(M 1) = −0, 000045 * 0, 2991103 = −0, 0000269  V$\begin{matrix}{I_{M\; 1.1} = \frac{V_{M\; 1}}{L_{9.2}*100\; \pi}} \\{= \frac{{- 0},{0000269*10^{6}}}{940*100\; \pi}} \\{{= {- 0}},{000091\mspace{14mu} A}}\end{matrix}$(The  current  passing  on  L_(9.2)  at  50  Hz)$\begin{matrix}{I_{M\; 2.1} = {V_{M\; 1}*C_{9.2}*100\; \pi}} \\{{= {- 0}},{0000269*{- 132}},{57*10^{- 6}*100\; \pi}} \\{{= 0},{000807\mspace{14mu} A}}\end{matrix}$(The  current  passing  on  C_(9.2)  at  50  Hz)V_(N 1) = I_((K − N)1) * x_(N 1) = −0, 00009 * 1, 3042857 = −0, 000117  V${V_{O\; 1} = 230},{{941401\mspace{14mu} V\mspace{14mu} {{idi}.{U_{O\; 1}}}} = {{\sqrt{3}*V_{O\; 1}} = 400}},{00224\mspace{14mu} V}$$\begin{matrix}{I_{L\; \Delta \; 1} = \frac{U_{O\; 1}}{L_{\Delta}*100\; \pi}} \\{= \frac{400,{00224*10^{6}}}{30550*100\; \pi}} \\{{= 41},{6607\mspace{14mu} A}}\end{matrix}$(The  current  passing  on  L_(Δ)  at  50  Hz)$\begin{matrix}{I_{C\; \Delta \; 1} = {U_{O\; 1}*C_{\Delta \; 1}*100\; \pi}} \\{{= 400},{00224*{- 331}},{4393*10^{- 6}*100\; \pi}} \\{{= {- 41}},{666888\mspace{14mu} A}}\end{matrix}$(The  current  passing  on  C_(Δ)  at  50  Hz)

     II-250  Hz      x_(A 5) = 570 * 10⁻⁶ * 500 π = 0, 895714${\frac{1}{x_{B\; 5}} = {\frac{10^{6}}{1530*500\; \pi} - 265}},{{15*10^{- 6}*500\; {\pi x_{B\; 5}}} = {- 1.878}},363188$$\mspace{79mu} {{\frac{1}{x_{C\; 5}} = {\frac{10^{6}}{470*500\; \pi} - 256}},{{15*10^{- 6}*500\; {\pi x_{C\; 5}}} = 1},066893}$$\mspace{79mu} {{\frac{1}{x_{D\; 5}} = {\frac{10^{6}}{320*500\; \pi} - 265}},{{15*10^{- 6}*500\; {\pi x_{D\; 5}}} = 0},636143}$     x_(E 5) = 790 * 10⁻⁶ * 500 π = 1, 241428     x_((B − E)5) = −1.875, 418724 

$\begin{matrix}{{\frac{1}{x_{F\; 5}} = {\frac{10^{6}}{2040*500\; \pi} - 198}},{8636*10^{- 6}*500\; {\pi x_{F\; 5}}}} \\{{= {- 1.795}},384175}\end{matrix}$${\frac{1}{x_{G\; 5}} = {\frac{10^{6}}{1040*500\; \pi} - 198}},{{8636*10^{- 6}*500\; {\pi x_{G\; 5}}} = 3},340145$${\frac{1}{x_{H\; 5}} = {\frac{10^{6}}{420*500\; \pi} - 198}},{{8636*10^{- 6}*500\; {\pi x_{H\; 5}}} = 0},831496$x_(I 5) = 1740 * 10⁻⁶ * 500 π = 2, 734285x_((F − I)5) = −1.788, 478249

$\begin{matrix}{{\frac{1}{x_{K\; 5}} = {\frac{10^{6}}{3060*500\; \pi} - 132}},{57*10^{- 6}*500\; {\pi x_{K\; 5}}}} \\{{= {- 2.760}},044138}\end{matrix}$${\frac{1}{x_{L\; 5}} = {\frac{10^{6}}{1560*500\; \pi} - 132}},{{57*10^{- 6}*500\; {\pi x_{L\; 5}}} = 5},009991$${\frac{1}{x_{M\; 5}} = {\frac{10^{6}}{940*500\; \pi} - 132}},{{57*10^{- 6}*500\; {\pi x_{M\; 5}}} = 2},13375$x_(N 5) = 4150 * 10⁻⁶ * 500 π = 6, 521428x_((K − N)5) = −2.746, 378969

$\mspace{79mu} \begin{matrix}{{\frac{1}{x_{O\; 5}} = {\frac{10^{6}}{10.183,{33*500\; \pi}} - 994}},{3179*10^{- 6}*500\; {\pi x_{O\; 5}}}} \\{{= {- 0}},666662}\end{matrix}$$\frac{1}{x_{{({A - N})}5}} = {\frac{1}{0,895714} + \frac{1}{1.875,418724} - \frac{1}{1.788,478249} - \frac{1}{2.746,378969}}$     x_((A − N)5) = 0, 896884     x₅ = 0, 896884 − 0, 666662 = 0, 230222$\mspace{79mu} {{I_{5} = {\frac{8,88}{0,230222} = 38}},{5714658\mspace{14mu} A}}$$\mspace{79mu} \begin{matrix}{V_{5} = {V_{A\; 5} + V_{O\; 5}}} \\{= {V_{B\; 5} + V_{C\; 5} + V_{D\; 5} + V_{E\; 5} + V_{O\; 5}}} \\{= {V_{F\; 5} + V_{G\; 5} + V_{H\; 5} + V_{I\; 5} + V_{O\; 5}}} \\{= {V_{K\; 5} + V_{L\; 5} + V_{M\; 5} + V_{N\; 5} + V_{O\; 5}}}\end{matrix}$

$\begin{matrix}{I_{A\; 5} = \frac{34,59413}{0,895714}} \\{{= 38},{621848\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{5}\mspace{14mu} {at}\mspace{14mu} 250\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{I_{{({B - E})}5} = \frac{34,59413}{{- 1.875},418724}} \\{{= {- 0}},{018446\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{7}\mspace{14mu} {at}\mspace{14mu} 250\mspace{14mu} {Hz}} \right)}\end{matrix}$ V_(B 5) = −0, 018446 * −1.878, 363188 = 34, 648287  V$\begin{matrix}{I_{B\; 1.5} = \frac{34,{648287*10^{6}}}{1560*500\; \pi}} \\{{= 14},{133916\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{5.1}\mspace{14mu} {at}\mspace{14mu} 250\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{B\; 2.5} = 34},{648287*{- 265}},{15*10^{- 6}*500\; \pi}} \\{{= {- 14}},{436703\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} C_{5.1}\mspace{14mu} {at}\mspace{14mu} 250\mspace{14mu} {Hz}} \right)}\end{matrix}$ V_(C 5) = −0, 018446 * 1, 066893 = −0, 0196799  V$\begin{matrix}{I_{C\; 1.5} = \frac{{- 0},{0196799*10^{6}}}{470*500\; \pi}} \\{{= {- 0}},{0266458\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{9.1}\mspace{14mu} {at}\mspace{14mu} 250\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{C\; 2.5} = {- 0}},{0196799*{- 265}},{15*10^{- 6}*500\; \pi}} \\{{= 0},{008199\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} C_{9.1}\mspace{14mu} {at}\mspace{14mu} 250\mspace{14mu} {Hz}} \right)}\end{matrix}\;$

V_(D 5) = −0, 018466 * 0, 636143 = −0, 011734  V $\begin{matrix}{I_{D\; 1.5} = \frac{{- 0},{011734*10^{6}}}{320*500\; \pi}} \\{{= {- 0}},{023334\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{11.1}\mspace{14mu} {at}\mspace{14mu} 250\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{D\; 2.5} = {- 0}},{011734*{- 265}},{15*10^{- 6}*500\; \pi}} \\{{= 0},{004889\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} C_{11.1}\mspace{14mu} {at}\mspace{14mu} 250\; {hz}} \right)}\end{matrix}$ V_(E 5) = −0, 018446 * 1, 241428 = −0, 022899  V 

$\begin{matrix}{I_{{({F - I})}5} = \frac{34,59413}{{- 1.788},478249}} \\{{= {- 0}},{019342\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{9}\mspace{14mu} {at}\mspace{14mu} 250\mspace{14mu} {Hz}} \right)}\end{matrix}$ V_(F 5) = −0, 019342 * −1.795, 384175 = 34, 72632  V$\begin{matrix}{I_{F\; 1.5} = \frac{34,{72632*10^{6}}}{2040*500\; \pi}} \\{{= 10},{832631\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{5.2}\mspace{14mu} {at}\mspace{14mu} 250\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{F\; 2.5} = 34},{72632*{- 198}},{8636*10^{- 6}*500\; \pi}} \\{{= {- 10}},{851973\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} C_{5.2}\mspace{14mu} {at}\mspace{14mu} 250\mspace{14mu} {Hz}} \right)}\end{matrix}$ V_(G 5) = −0, 019342 * 3, 340145 = −0, 064605  V$\begin{matrix}{I_{G\; 1.5} = \frac{{- 0},{064605*10^{6}}}{1040*500\; \pi}} \\{{= {- 0}},{039531\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{7.1}\mspace{14mu} {at}\mspace{14mu} 250\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{G\; 2.5} = {- 0}},{064605*{- 198}},{8636*10^{- 6}*500\; \pi}} \\{{= 0},{020189\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} C_{7.1}\mspace{14mu} {at}\mspace{14mu} 250\mspace{14mu} {Hz}} \right)}\end{matrix}$ V_(H 5) = −0, 019342 * 0, 831496 = −0, 016082  V$\begin{matrix}{I_{H\; 1.5} = \frac{{- 0},{016082*10^{6}}}{420*500\; \pi}} \\{{= {- 0}},{024366\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{11.2}\mspace{14mu} {at}\mspace{14mu} 250\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{H\; 2.5} = {- 0}},{016082*{- 198}},{8636*10^{- 6}*500\; \pi}} \\{{= 0},{005025\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} C_{11.2}\mspace{14mu} {at}\mspace{14mu} 250\mspace{14mu} {Hz}} \right)}\end{matrix}$

V_(I.5) = −0, 019342 * 2, 734285 = −0, 052886  V $\begin{matrix}{I_{{({K - N})}5} = \frac{34,59413}{{- 276},378969}} \\{{= {- 0}},{012596\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{11}\mspace{14mu} {at}\mspace{14mu} 250\mspace{14mu} {Hz}} \right)}\end{matrix}$ V_(K 5) = −0, 012596 * −2760, 044138 = 34, 765515  V$\begin{matrix}{I_{K\; 1.5} = \frac{34,{765515*10^{6}}}{3060*500\; \pi}} \\{{= 7},{229905\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{5.3}\mspace{14mu} {at}\mspace{14mu} 250\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{K\; 2.5} = 34},{765515*{- 132}},{57*10^{- 6}*500\; \pi}} \\{{= {- 7}},{242501\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} C_{5.3}\mspace{14mu} {at}\mspace{14mu} 250\mspace{14mu} {Hz}} \right)}\end{matrix}$ V_(L 5) = −0, 012596 * 5, 009991 = −0, 631058  V$\begin{matrix}{I_{L\; 1.5} = \frac{{- 0},{631058*10^{6}}}{1560*500\; \pi}} \\{{= {- 0}},{257424\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{7.2}\mspace{14mu} {at}\mspace{14mu} 250\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{L\; 2.5} = {- 0}},{631058*{- 132}},{57*10^{- 6}*500\; \pi}} \\{{= 0},{131473\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} C_{7.2}\mspace{14mu} {at}\mspace{14mu} 250\mspace{14mu} {Hz}} \right)}\end{matrix}$

V_(M 5) = −0, 012596 * 2, 13375 = −0, 026876  V $\begin{matrix}{I_{M\; 1.5} = \frac{{- 0},{026876*10^{6}}}{940*500\; \pi}} \\{{= {- 0}},{018194\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{9.2}\mspace{14mu} {at}\mspace{14mu} 250\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{M\; 2.5} = {- 0}},{026876*{- 132}},{57*10^{- 6}*500\; \pi}} \\{{= 0},{005598\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} C_{9.2}\mspace{14mu} {at}\mspace{14mu} 250\mspace{14mu} {Hz}} \right)}\end{matrix}$ V_(N 5) = −0, 012596 * 6, 521428 = −0, 0821439  VV_(O 5) = −25, 71413  V  idi.U_(O 5) = −44, 538179  V$\begin{matrix}{I_{L\; \Delta \; 5} = \frac{{- 44},{538179*10^{6}}}{30550*500\; \pi}} \\{{= {- 0}},{92774\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{\Delta}\mspace{14mu} {at}\mspace{14mu} 250\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{C\; \Delta \; 5} = {- 44}},{538179*{- 331}},{4393*10^{- 6}*500\; \pi}} \\{{= 23},{196961\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} C_{\Delta}\mspace{14mu} {at}\mspace{14mu} 250\mspace{14mu} {Hz}} \right)}\end{matrix}$

III-350  Hz  x_(A 7) = 570 * 10⁻⁶ * 700 π = 1, 254${\frac{1}{x_{B\; 7}} = {\frac{10^{6}}{1530*700\; \pi} - 265}},{{15*10^{- 6}*700\; {\pi x_{B\; 7}}} = {- 3}},493553$${\frac{1}{x_{C\; 7}} = {\frac{10^{6}}{470*700\; \pi} = {- 256}}},{{15*10^{- 6}*700\; {\pi x_{C\; 7}}} = 2},605605$${\frac{1}{x_{D\; 7}} = {\frac{10^{6}}{320*700\; \pi} - 265}},{{15*10^{- 6}*700\; {\pi x_{D\; 7}}} = 1},194565$x_(E 7) = 790 * 10⁻⁶ * 700 π = 1, 738 x_((B − E)7) = 2, 044617

$\begin{matrix}{{\frac{1}{x_{F\; 7}} = {\frac{10^{6}}{2040*700\; \pi} - 198}},{8636*10^{- 6}*700\; {\pi x_{F\; 7}}}} \\{{= {- 4}},658019}\end{matrix}$ $\begin{matrix}{{\frac{1}{x_{G\; 7}} = {\frac{10^{6}}{1040*700\; \pi} - 198}},{8636*10^{- 6}*700\; {\pi x_{G\; 7}}}} \\{{= {- 2.288}},4188719}\end{matrix}$ $\begin{matrix}{{\frac{1}{x_{H\; 7}} = {\frac{10^{6}}{420*700\; \pi} - 198}},{8636*10^{- 6}*700\; {\pi x_{H\; 7}}}} \\{{= 1},550985}\end{matrix}$ x_(I 7) = 1740 * 10⁻⁶ * 700 π = 3, 828x_((F − I)7) = −2.287, 6979059

$\mspace{79mu} {{\frac{1}{x_{K\; 7}} = {\frac{10^{6}}{3060*700\; \pi} - 132}},{{57*10^{- 6}*700\; {\pi x_{K\; 7}}} = {- 6}},987644}$$\mspace{79mu} \begin{matrix}{{\frac{1}{x_{L\; 7}} = {\frac{10^{6}}{1560*700\; \pi} - 132}},{57*10^{- 6}*700\; {\pi x_{L\; 7}}}} \\{{= {- 3587}},976513}\end{matrix}$ $\mspace{79mu} \begin{matrix}{{\frac{1}{x_{M\; 7}} = {\frac{10^{6}}{940*700\; \pi} - 132}},{57*10^{- 6}*700\; {\pi x_{M\; 7}}}} \\{{= 5},2109118}\end{matrix}$      x_(N 7) = 4150 * 10⁻⁶ * 700 π = 9, 13     x_((K − N)7) = −3580, 623245 $\mspace{76mu} \begin{matrix}{{\frac{1}{x_{O\; 7}} = {\frac{10^{6}}{10.183,{33*700\; \pi}} - 994}},{3179*10^{- 6}*700\; {\pi x_{O\; 7}}}} \\{{= {- 0}},466665}\end{matrix}$${\frac{1}{x_{{({A - N})}7}} = {\frac{1}{1,254} + \frac{1}{2,044617} - \frac{1}{2.287,6979059} - \frac{1}{3.580,623245}}}\;$

x_((A − N)7) = 0, 777713 x₇ = 0, 777713 − 0, 466665 = 0, 311048${I_{7} = {\frac{15,55}{0,311048} = 49}},{992284\mspace{14mu} A}$$\begin{matrix}{V_{7} = {V_{A\; 7} + V_{O\; 7}}} \\{= {V_{B\; 7} + V_{C\; 7} + V_{D\; 7} + V_{E\; 7} + V_{O\; 7}}} \\{= {V_{F\; 7} + V_{G\; 7} + V_{H\; 7} + V_{I\; 7} + V_{O\; 7}}} \\{= {V_{K\; 7} + V_{L\; 7} + V_{M\; 7} + V_{N\; 7} + V_{O\; 7}}}\end{matrix}$ $\begin{matrix}{I_{A7} = \frac{38,879649}{1,254}} \\{{= 31},{004504\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{5}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{I_{{({B - E})}7} = \frac{38,879649}{2,044617}} \\{{= 19},{015614\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{7}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$ V_(B 7) = 19, 015614 * −3, 493553 = −66, 432055  V$\begin{matrix}{I_{B\; 1.7} = \frac{{- 66},{432055*10^{6}}}{1560*700\; \pi}} \\{{= {- 19}},{356659\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{5.1}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{B\; 2.7} = {- 66}},{432055*{- 265}},{15*10^{- 6}*700\; \pi}} \\{{= 38},{75181\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} C_{5.1}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$

 V_(C 7) = 19, 015614 * 2, 605605 = 50, 506421  V $\begin{matrix}{I_{C\; 1.7} = \frac{50,{506421*10^{6}}}{470*700\; \pi}} \\{{= 48},{845668\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{9.1}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{C\; 2.7} = 50},{506421*{- 265}},{15*10^{- 6}*700\; \pi}} \\{{= {- 29}},{46191\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} C_{9.1}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$ V_(D 7) = 19, 015614 * 1, 194565 = 22, 715386  V$\begin{matrix}{I_{D\; 1.7} = \frac{22,{715386*10^{6}}}{320*700\; \pi}} \\{{= 32},{266173\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{11.1}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{D\; 2.7} = 22},{715386*{- 265}},{15*10^{- 6}*700\; \pi}} \\{{= {- 13}},{250566\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} C_{11.1}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$ V_(E 7) = 19, 015614 * 1, 738 = 33, 049137  V

$\begin{matrix}{I_{{({F - I})}7} = \frac{38,879649}{{- 2.287},6979059}} \\{{= {- 0}},{016995\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{9}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$ V_(F 7) = −0, 016995 * −4, 658019 = 0, 079463  V$\begin{matrix}{I_{F\; 1.7} = \frac{0,{079463*10^{6}}}{2040*700\; \pi}} \\{{= 0},{017638\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{5.2}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{F\; 2.7} = 0},{079163*{- 198}},{8636*10^{- 6}*700\; \pi}} \\{{= {- 0}},{034633\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} C_{5.2}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$ V_(G 7) = −0, 016995 * −2.288, 4188719 = 38, 891678  V$\begin{matrix}{I_{G\; 1.7} = \frac{38,{891678*10^{6}}}{1040*700\; \pi}} \\{{= 16},{998111\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{7.1}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{G\; 2.7} = 38},{891678*{- 198}},{8636*10^{- 6}*700\; \pi}} \\{{= {- 17}},{01506\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} C_{7.1}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$

V_(H 7) = −0, 016995 * 1, 550985 = −0, 026358  V $\begin{matrix}{I_{H\; 1.7} = \frac{{- 0},{026358*10^{6}}}{420*700\; \pi}} \\{{= {- 0}},{0285259\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{11.2}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{H\; 2.7} = {- 0}},{026358*{- 198}},{8636*10^{- 6}*700\; \pi}} \\{{= 0},{011531\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} C_{11.2}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$ V_(I.7) = −0, 016995 * 3, 828 = −0, 065056  V$\begin{matrix}{I_{{({K - N})}7} = \frac{38,879649}{{- 3.580},623245}} \\{{= {- 0}},{010858\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{11}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$

V_(K 7) = −0, 010858 * −6, 987644 = 0, 075871  V $\begin{matrix}{I_{K\; 1.7} = \frac{0,{075871*10^{6}}}{3060*700\; \pi}} \\{{= 0},{01127\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{5.3}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{K\; 2.7} = 0},{075871*{- 132}},{57*10^{- 6}*700\; \pi}} \\{{= {- 0}},{022128\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} C_{5.3}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$ V_(L 7) = −0, 010858 * 3.587, 976513 = 38, 958248  V$\begin{matrix}{I_{L\; 1.7} = \frac{38,{958248*10^{6}}}{1560*700\; \pi}} \\{{= 11},{35147\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{7.2}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{L\; 2.7} = 38},{958248*{- 132}},{57*10^{- 6}*700\; \pi}} \\{{= {- 11}},{362328\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} C_{7.2}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$

V_(M 7) = −0, 010858 * 5, 2109118 = −0, 05658  V $\begin{matrix}{I_{M\; 1.7} = \frac{{- 0},{05658*10^{6}}}{940*700\; \pi}} \\{{= {- 0}},{027359\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{9.2}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{M\; 2.7} = {- 0}},{05658*{- 132}},{57*10^{- 6}*700\; \pi}} \\{{= 0},{0165017\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} C_{9.2}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$ V_(N 7) = −0, 010858 * 9, 13 = −0, 099133  VV_(O 7) = −23, 329649  V  idi.U_(O 7) = −40, 408137  V$\begin{matrix}{I_{L\; \Delta \; 7} = \frac{{- 40},{408137*10^{6}}}{30550*700\; \pi}} \\{{= {- 0}},{601222\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{\Delta}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{C\; \Delta \; 7} = {- 40}},{408137*{- 331}},{4393*10^{- 6}*700\; \pi}} \\{{= 29},{464258\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} C_{\Delta}\mspace{14mu} {at}\mspace{14mu} 350\mspace{14mu} {Hz}} \right)}\end{matrix}$

$\begin{matrix}{{{{{x_{A9} = {{570*10^{- 6}*900\pi} = 1}},612285}\frac{1}{x_{B\; 9}} = {\frac{10^{6}}{1530*900\pi} - 265}},{{15*10^{- 6}*900{\pi x_{B\; 9}}} = {- 1}},927053}{{\frac{1}{x_{C\; 9}} = {\frac{10^{6}}{470*900\pi} = {- 256}}},{{15*10^{- 6}*900{\pi x_{C\; 9}}} = 453},069769}{{\frac{1}{x_{D\; 9}} = {\frac{10^{6}}{320*900\pi} - 265}},{{15*10^{- 6}*900{\pi x_{D\; 9}}} = 2},818471}{{x_{E\; 9} = {{790*10^{- 6}*900\pi} = 2}},234571}{{x_{{({B - E})}9} = 456},195758}} & {{IV}\text{-}450\mspace{14mu} {Hz}}\end{matrix}$

${\frac{1}{x_{F\; 9}} = {\frac{10^{6}}{2040*900\pi} - 198}},{{8636*10^{- 6}*900{\pi x_{F\; 9}}} = {- 2}},569384$${\frac{1}{x_{G\; 9}} = {\frac{10^{6}}{1040*900\pi} - 198}},{{8636*10^{- 6}*900{\pi x_{G\; 9}}} = {- 4}},493128$${\frac{1}{x_{H\; 9}} = {\frac{10^{6}}{420*900\pi} - 198}},{{8636*10^{- 6}*900{\pi x_{H\; 9}}} = 3},581008$x_(I 9) = 1740 * 10⁻⁶ * 900π = 4, 921714 x_((F − I)9) = 1, 44021${\frac{1}{x_{k\; 9}} = {\frac{10^{6}}{3060*900\pi} - 132}},{{57*10^{- 6}*900{\pi x_{K\; 9}}} = {- 3}},854317$${\frac{1}{x_{L\; 9}} = {\frac{10^{6}}{1560*900\pi} - 132}},{{57*10^{- 6}*900{\pi x_{L\; 9}}} = {- 6}},740429$${\frac{1}{x_{M\; 9}} = {\frac{10^{6}}{940*900\pi} - 132}},{{57*10^{- 6}*900{\pi x_{M\; 9}}} = 894},673933$

x_(N 9) = 4150 * 10⁻⁶ * 900π = 11, 738571 x_((K − N)9) = 895, 817758${\frac{1}{x_{O\; 9}} = {\frac{10^{6}}{10.183,{33*900\pi}} - 994}},{{317 9*10^{- 6}*900{\pi x_{O\; 9}}} = {- 0}},{{359999\frac{1}{x_{{({A - N})}9}}} = {\frac{1}{1,612285} - \frac{1}{456,195758} + \frac{1}{1,44021} + {\frac{1}{895,817758}{x_{{({A - N})}9} = 0}}}},{758789{x_{9} = 0}},{758789 - 0},{359999 = 0},{38879{I_{9} = {\frac{11,99}{0,38879} = 30}}},{83927\mspace{14mu} A\begin{matrix}{V_{9} = {V_{A\; 9} + V_{O\; 9}}} \\{= {V_{B\; 9} + V_{C\; 9} + V_{D\; 9} + V_{E\; 9} + V_{O\; 9}}} \\{= {{V_{F\; 9} + V_{G\; 9} + V_{H\; 9} + V_{I\; 9} + V_{O\; 9}} =}} \\{= {V_{K\; 9} + V_{L\; 9} + V_{M\; 9} + V_{N\; 9} + V_{O\; 9}}}\end{matrix}}$

V_(O 9) = 30, 83927 * −0, 359999 = −11, 102106V_(A 9) = 11, 99 + 11, 102106 = 23, 092106${I_{A\; 9} = {\frac{23,092106}{1,612285} = 14}},{32259519\mspace{14mu} {A\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{5}\mspace{14mu} {at}\mspace{14mu} 450\mspace{11mu} {Hz}} \right)}}$${I_{{({B - E})}9} = {\frac{23,092106}{456,195758} = 0}},{050618\mspace{14mu} {A\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{7}\mspace{11mu} {at}\mspace{11mu} 450\mspace{14mu} {Hz}} \right)}}$V_(B 9) = 0, 050618 * −1, 927053 = −0, 097543  V${I_{B\; 1.9} = {\frac{{- 0},{097543*10^{6}}}{1560*900\pi} = {- 0}}},{022105\mspace{14mu} {A\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{5.1}\mspace{14mu} {at}\mspace{14mu} 450\mspace{14mu} {Hz}} \right)}}$I_(B 2.9) = −0, 097543 * −265, 15 * 10⁻⁶ * 900π = 0, 073156  A(The  current  passing  on  C_(5.1)  at  450  Hz)V_(C 9) = 0, 050618 * 453, 069769 = 22, 933485  V${I_{C\; 1.9} = {\frac{22,{933485*10^{6}}}{470*900\pi} = 17}},{250633\mspace{14mu} {A\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{9.1}\mspace{14mu} {at}\mspace{14mu} 450\mspace{14mu} {Hz}} \right)}}$I_(C 2.9) = 22, 933485 * −265, 15 * 10⁻⁶ * 900π = −17, 200015  A(The  current  passing  on  C_(9.1)  at  450  Hz)

V_(D 9) = 0, 050618 * 2, 818471 = 0, 142665  V${I_{D\; 1.9} = {\frac{0,{142665*10^{6}}}{320*900\pi} = 0}},157616\mspace{14mu} {A\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{11.1}\mspace{14mu} {at}\mspace{14mu} 450\mspace{14mu} {Hz}} \right)}$I_(D 2.9) = 0, 142665 * −265, 15 * 10⁻⁶ * 900π = −0, 106998  A(The  current  passing  on  C_(11.1)  at  450  Hz)V_(E 9) = 0, 050618 * 2, 234571 = 0, 113109  V${I_{{({F - I})}9} = {\frac{23,092106}{1,44021} = 16}},{033846\mspace{14mu} {A\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{9}\mspace{14mu} {at}\mspace{14mu} 450\mspace{14mu} {Hz}} \right)}}$V_(F 9) = 16, 033846 * −2, 569384 = −41, 197107  V${I_{F\; 1.9} = {\frac{{- 41},{197107*10^{6}}}{2040*900\pi} = {- 7}}},{139526\mspace{14mu} {A\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{5.2}\mspace{14mu} {at}\mspace{14mu} 450\mspace{14mu} {Hz}} \right)}}$I_(F 2.9) = −41, 197107 * −198, 8636 * 10⁻⁶ * 900π = 23, 173368  A(The  current  passing  on  C_(5.2)  at  450  Hz)V_(G 9) = 16, 033846 * −4, 493128 = −72, 042122  V

${I_{G\; 1.9} = {\frac{{- 72},{042122*10^{6}}}{1040*900\pi} = {- 24}}},489843\mspace{14mu} {A\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{7.1}\mspace{14mu} {at}\mspace{14mu} 450\mspace{14mu} {Hz}} \right)}$I_(G 2.9) = −72, 042122 * −198, 8636 * 10⁻⁶ * 900π = 40, 523686  A(The  current  passing  on  C_(7.1)  at  450  Hz)V_(H 9) = 16, 033846 * 3, 581008 = 57, 41733  V${I_{H\; 1.9} = {\frac{57,{41733*10^{6}}}{420*900\pi} = 48}},{331085\mspace{14mu} {A\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{11.2}\mspace{14mu} {at}\mspace{14mu} 450\mspace{14mu} {Hz}} \right)}}$I_(H 2.9) = 57, 41733 * −198, 8636 * 10⁻⁶ * 900π = 40, 523686  A(The  current  passing  on  C_(11.2)  at  450  Hz)V_(I.9) = 16, 033846 * 4, 921714 = 78, 914004  V${I_{{({K - N})}9} = {\frac{23,092106}{895,817758} = 0}},{025777\mspace{14mu} {A\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{11}\mspace{14mu} {at}\mspace{14mu} 450\mspace{14mu} {Hz}} \right)}}$

V_(K 9) = 0, 025777 * −3, 854317 = −0, 099352  V${I_{K\; 1.9} = {\frac{{- 0},{099352*10^{6}}}{3060*900\pi} = {- 0}}},011478\mspace{14mu} {A\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{5.3}\mspace{14mu} {at}\mspace{14mu} 450\mspace{14mu} {Hz}} \right)}$I_(K 2.9) = −0, 099352 * −132, 57 * 10⁻⁶ * 900π = 0, 037255  A(The  current  passing  on  C_(5.3)  at  450  Hz)V_(L 9) = 0, 025777 * −6, 740429 = −0, 173748  V${I_{L\; 1.9} = {\frac{{- 0},{173748*10^{6}}}{1560*900\pi} = {- 0}}},{039375\mspace{14mu} {A\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{7.2}\mspace{14mu} {at}\mspace{14mu} 450\mspace{14mu} {Hz}} \right)}}$I_(L 2.9) = 0, 173748 * 894, 673933 * 10⁻⁶ * 900π = 0, 065122  A(The  current  passing  on  C_(7.2)  and  at  450  Hz)

V_(M 9) = 0, 025777 * 894, 673933 = 23, 062009  V${I_{M\; 1.9} = {\frac{23,{062009*10^{6}}}{940*900\pi} = 8}},673654\mspace{14mu} {A\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{9.2}\mspace{14mu} {at}\mspace{14mu} 450\mspace{14mu} {Hz}} \right)}$I_(M 2.9) = 23, 062009 * −132, 57 * 10⁻⁶ * 900π = −8, 647877  A(The  current  passing  on  C_(9.2)  at  450  Hz)V_(N 9) = 0, 025777 * 11, 738571 = 0, 302585  VV_(O 9) = −11, 102106  V  idi.U_(O 9) = −19, 229411  V${I_{L\; \Delta \; 9} = {\frac{{- 19},{229411*10^{6}}}{30550*900\pi} = {- 0}}},{222529\mspace{14mu} {A\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}\mspace{14mu} {on}\mspace{14mu} L_{\Delta}\mspace{14mu} {at}\mspace{14mu} 450\mspace{14mu} {Hz}} \right)}}$I_(C Δ 9) = −19, 229411 * −331, 4393 * 10⁻⁶ * 900π = 18, 027567  A(The  current  passing  on  C_(Δ)  at  450  Hz)

V-550  Hz x_(A 11) = 570 * 10⁻⁶ * 1100 π = 1, 970571$\begin{matrix}{{\frac{1}{x_{B\; 11}} = {\frac{10^{6}}{1530*1100\; \pi} - 265}},{15*10^{- 6}*1100\; {\pi x_{B\; 11}}}} \\{{= {- 1}},374371}\end{matrix}$ $\begin{matrix}{{\frac{1}{x_{C\; 11}} = {\frac{10^{6}}{470*1100\; \pi} = {- 256}}},{15*10^{- 6}*1100\; {\pi x_{C\; 11}}}} \\{{= {- 3}},319802}\end{matrix}$ $\begin{matrix}{{\frac{1}{x_{D\; 11}} = {\frac{10^{6}}{320*1100\; \pi} - 265}},{15*10^{- 6}*1100\; {\pi x_{D\; 11}}}} \\{{= {- 78}},518767}\end{matrix}$ x_(E 11) = 790 * 10⁻⁶ * 1100 π = 2, 731142x_((B − E)11) = −80, 481798 $\begin{matrix}{{\frac{1}{x_{F\; 11}} = {\frac{10^{6}}{2040*1100\; \pi} - 198}},{8636*10^{- 6}*1100\; {\pi x_{F\; 11}}}} \\{{= {- 1}},832483}\end{matrix}$ $\begin{matrix}{{\frac{1}{x_{G\; 11}} = {\frac{10^{6}}{1040*1100\; \pi} - 198}},{8636*10^{- 6}*1100\; {\pi x_{G\; 11}}}} \\{{= {- 2}},442874}\end{matrix}$

$\begin{matrix}{{\frac{1}{x_{H\; 11}} = {\frac{10^{6}}{420*1100\; \pi} - 198}},{8636*10^{- 6}*1100\; {\pi x_{H\; 11}}}} \\{{= 829},627749}\end{matrix}$ x_(I 11) = 1740 * 10⁻⁶ * 1100 π = 6, 015428x_((F − I)11) = 831, 36791 $\begin{matrix}{{\frac{1}{x_{K\; 11}} = {\frac{10^{6}}{3060*1100\; \pi} - 132}},{57*10^{- 6}*1100\; {\pi x_{K\; 11}}}} \\{{= {- 2}},748874}\end{matrix}$ $\begin{matrix}{{\frac{1}{x_{L\; 11}} = {\frac{10^{6}}{1560*1100\; \pi} - 132}},{57*10^{- 6}*1100\; {\pi x_{L\; 11}}}} \\{{= {- 3}},664442}\end{matrix}$ $\begin{matrix}{{\frac{1}{x_{M\; 11}} = {\frac{10^{6}}{940*1100\; \pi} - 132}},{57*10^{- 6}*1100\; {\pi x_{M\; 11}}}} \\{{= {- 6}},640367}\end{matrix}$ x_(N 11) = 4150 * 10⁻⁶ * 1100 π = 14, 347142x_((K − N)11) = 1, 293459

$\begin{matrix}{{\frac{1}{x_{O\; 11}} = {\frac{10^{6}}{10.183,{33*1100\; \pi}} - 994}},{3179*10^{- 6}*1100\; {\pi x_{O\; 11}}}} \\{{= {- 0}},293333}\end{matrix}$$\frac{1}{x_{{({A - N})}11}} = {\frac{1}{1,970571} - \frac{1}{80,481798} + \frac{1}{831,36791} + \frac{1}{1,293459}}$x_((A − N)11) = 0, 787795 x₁₁ = 0, 787795 − 0, 293333 = 0, 494462${I_{11} = {\frac{9,77}{0,494462} = 19}},{758849\mspace{14mu} A}$

$\begin{matrix}{V_{11} = {V_{A\; 11} + V_{O\; 11}}} \\{= {V_{B\; 11} + V_{C\; 11} + V_{D\; 11} + V_{E\; 11} + V_{O\; 11}}} \\{= {V_{F\; 11} + V_{G\; 11} + V_{H\; 11} + V_{I\; 11} + V_{O\; 11}}} \\{= {V_{K\; 11} + V_{L\; 11} + V_{M\; 11} + V_{N\; 11} + V_{O\; 11}}}\end{matrix}$ V_(O 11) = 19, 758849 * −0, 293333 = −5, 795922  VV_(A 11) = 9, 77 + 5, 795922 = 15, 565922  V $\begin{matrix}{I_{A\; 11} = \frac{15,565922}{1,970571}} \\{{= 7},{899193\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} L_{5}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{I_{{({B - E})}11} = \frac{15,565922}{{- 80},481798}} \\{{= {- 0}},{193409\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} L_{7}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}\end{matrix}$ V_(B 11) = −0, 193409 * −1, 374371 = 0, 265815  V$\begin{matrix}{I_{B\; 1.11} = \frac{0,{265815*10^{6}}}{1560*1100\; \pi}} \\{{= 0},{012191\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} L_{5.1}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{B\; 2.11} = 0},{265815*{- 265}},{15*10^{- 6}*1100\; \pi}} \\{{= {- 0}},{243662\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} C_{5.1}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}\end{matrix}$

V_(C 11) = −0, 193409 * −3, 319802 = 0, 642079  V $\begin{matrix}{I_{C\; 1.11} = \frac{0,{642079*10^{6}}}{470*1100\; \pi}} \\{{= 0},{39516\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} L_{9.1}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{C\; 2.11} = 0},{642079*{- 265}},{15*10^{- 6}*1100\; \pi}} \\{{= {- 0}},{588569\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} C_{9.1}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}\end{matrix}$ V_(D 11) = −0, 193409 * −78, 518767 = 15, 186236  V$\begin{matrix}{I_{D\; 1.11} = \frac{15,{186236*10^{6}}}{320*1100\; \pi}} \\{{= 13},{727227\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} L_{11.1}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{D\; 2.11} = 15},{186236*{- 265}},{15*10^{- 6}*1100\; \pi}} \\{{= {- 13}},{920636\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} C_{11.1}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}\end{matrix}$ V_(E 11) = −0, 193409 * 2, 731142 = −0, 528227  V

$\quad{{{\begin{matrix}{I_{{({F - I})}11} = \frac{15,565922}{831,36791}} \\{{= 0},{018723\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} L_{9}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}\end{matrix}V_{F\; 11}} = 0},{018723*{- 1}},{832483 = {--0}},{{0343095\mspace{14mu} V\begin{matrix}{I_{F\; 1.11} = \frac{{- 0},{0343095*10^{6}}}{2040*1100\; \pi}} \\{{= {- 0}},{00486\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} L_{5.2}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}\end{matrix}\begin{matrix}{{I_{F\; 2.11} = {- 0}},{0343095*{- 198}},{8636*10^{- 6}*1100\; \pi}} \\{{= 0},{023587\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} C_{5.2}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}\end{matrix}V_{G\; 11}} = 0},{018723*{- 2}},{442784 = {- 0}},{045736\mspace{14mu} V\begin{matrix}{I_{G\; 1.11} = \frac{{- 0},{045736*10^{6}}}{1040*1100\; \pi}} \\{{= {- 0}},{01272\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} L_{7.1}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}\end{matrix}\begin{matrix}{{I_{G\; 2.11} = {- 0}},{045736*{- 198}},{8636*10^{- 6}*1100\; \pi}} \\{{= 0},{031443\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} C_{7.1}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}\end{matrix}}}$

V_(H 11) = 0, 018723 * 829, 627749 = 15, 53312  V $\begin{matrix}{I_{H\; 1.11} = \frac{15,{53312*10^{6}}}{420*1100\; \pi}} \\{= {A\mspace{14mu} \left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} L_{11.2}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}}\end{matrix}$ $\begin{matrix}{{I_{H\; 2.11} = 15},{53312*{- 198}},{8636*10^{- 6}*1100\; \pi}} \\{{= {- 10}},{679018\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} C_{11.2}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}\end{matrix}$ V_(I.11) = 0, 018723 * 6, 015428 = 0, 112626  V$\begin{matrix}{I_{{({K - N})}11} = \frac{15,565922}{1,293459}} \\{{= 12},{034337\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} L_{11}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}\end{matrix}$ V_(K 11) = 12, 034337 * −2, 748874 = −33, 080876  V$\begin{matrix}{I_{K\; 1.11} = \frac{{--33},{080876*10^{6}}}{3060*1100\; \pi}} \\{{= {- 3}},{127074\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} L_{5.3}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{K\; 2.11} = {- 33}},{080876*{- 132}},{57*10^{- 6}*1100\; \pi}} \\{{= 15},{161409\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} C_{5.3}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}\end{matrix}$

V_(L 11) = 12, 034337 * −3, 664442 = −44, 099129  V $\begin{matrix}{I_{L\; 1.11} = \frac{{- 44},{099129*10^{6}}}{1560*1100\; \pi}} \\{{= {- 8}},{176888\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} L_{7.2}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{L\; 2.11} = {- 44}},{099129*{- 132}},{57*10^{- 6}*1100\; \pi}} \\{{= 20},{211223\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} C_{7.2}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}\end{matrix}$ V_(M 11) = 12, 034337 * −6, 640367 = −79, 912414  V$\begin{matrix}{I_{M\; 1.11} = \frac{{- 79},{912414*10^{6}}}{940*1100\; \pi}} \\{{= {- 24}},{590596\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} L_{9.2}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}\end{matrix}$

$\begin{matrix}{{I_{M\; 2.11} = {- 79}},{912414*{- 132}},{57*10^{- 6}*1100\; \pi}} \\{{= 36},{624932\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} C_{9.2}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}\end{matrix}$ V_(N 11) = 12, 034337 * 14, 347142 = 172, 658341  VV_(O 11) = −5, 795922  V   idi.U_(O 11) = −10, 038831  V$\begin{matrix}{I_{L\; \Delta \; 11} = \frac{{- 10},{038831*10^{6}}}{30550*1100\; \pi}} \\{{= {- 0}},{09505\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} L_{\Delta}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}\end{matrix}$ $\begin{matrix}{{I_{C\; \Delta \; 11} = {- 10}},{038831*{- 331}},{4393*10^{- 6}*1100\; \pi}} \\{{= 11},{502823\mspace{14mu} A}} \\{\left( {{The}\mspace{14mu} {current}\mspace{14mu} {passing}{\mspace{11mu} \;}{on}\mspace{14mu} C_{\Delta}\mspace{14mu} {at}\mspace{14mu} 550\mspace{14mu} {Hz}} \right)}\end{matrix}$

If we list the values we have found and the characteristics of thematerials: The scope of protection for this application is to bedetermined by the claims, and can certainly not be limited to thoseexplained above for exemplary purposes. It is clear that the innovationput forward by a technical expert in the invention, can also be putforward by using similar structures and/or this structure may be appliedin other fields with similar purposes used in the related technique.Therefore, it is evident that such structures shall lack the criteria ofovercoming the innovation and especially, the existing condition of thetechnique.

1. A harmonic absorber for eliminating the harmonics that occur due tonon-linear loads, in a system comprising at least one networktransformer, preferably a power factor correction, in order to correctthe cos φ value of the system at which it has been connected andelectrical loads characterized in that the absorber consists of at leastone harmonic hole circuit that damps the harmonic current or currentsapplied to it and a harmonic separator circuit, which separates theharmonic currents existing in the network from the other components ofthe network and then applies each resultant individual harmonic currentto said harmonic hole circuit in order that its elimination can beachieved.
 2. A harmonic absorber according to claim 1, characterised inthat the harmonic hole circuit constitutes a delta connection with ofbarrier circuits comprising power reactance inductors and powercapacitors parallel to each other.
 3. A harmonic absorber according toclaim 1, wherein the harmonic hole circuit forms a star connection ofbarrier circuits, which consist of power reactance inductors and powercapacitors connected parallel to each other.
 4. A harmonic absorberaccording to claim 1, characterised in that the harmonic hole circuitcomprises parallel power reactance inductors and power capacitors, towhich each individual harmonic current is applied separately.
 5. Aharmonic absorber according to claim 1, containing harmonic barriercircuits in the same number as the harmonic currents, which are requiredto be suppressed.
 6. A harmonic absorber according to claim 1, includingat least one power reactance inductor for attracting a harmonic current,which is required to be damped, to said harmonic separator and thentransferring the harmonic current directly to said harmonic hole.
 7. Aharmonic absorber according to claim 1, comprising serially connectedharmonic barrier circuits, the number of which is determined accordingto the required sensitivity for conducting only the harmonic, whoseelimination is desired, and barring the other harmonics.
 8. A harmonicabsorber according to claim 7, having harmonic barrier circuitscomprising power reactance inductors and power capacitors, whose valuesare calculated in accordance with the components of the harmonic currentthat is requested to be eliminated and which are connected in parallel.9. A method for absorbing the harmonics that occur due to non-linearloads, in a network comprising at least one network transformer,preferably including a power factor correction, in order to correct thecos φ value of the system to which it has been connected and electricalloads, the method being characterized by: obtaining individual harmoniccurrents by separating the harmonic currents, which, for the system,have to be eliminated from the network and from each other, using atleast one harmonic separator and damping the harmonic currents thusseparated, by using at least one harmonic hole.
 10. A method accordingto claim 9, wherein to eliminate the harmonics that are formed in thenetwork, all harmonic currents except the ones which are required to beattracted via the harmonic separator are filtered via harmonic barriersin order to obtain the harmonic currents.
 11. A method according toclaim 9, wherein to eliminate the harmonics that are formed in thenetwork, the harmonic current, which is required to be damped, isattracted to said harmonic hole via at least one harmonic transferor, inorder to obtain the harmonic currents.
 12. A method according to claim11, wherein the harmonic transferor comprises at least one powerreactance inductor, whose values are calculated for drawing thealternative signal at the requested frequency.
 13. A method according toclaim 9, wherein to eliminate the harmonics that occur in the network,said harmonic separator and harmonic hole, which constitute the harmonicabsorber, are connected to a connection point directly after the mainswitch and directly before all other elements in the system, to protectthe system.